I want at least one glitch Pokemon but I don't know where to find them and how rare they are.
I have encountered a ----- on Pearl, but I have not encountered glitch Pokemon on White. I have never encountered glitch Pokemon ever in my life before except on Pearl and I want one glitch on White!

Note:

I have never seen any other glitch Pokemon except -----, so you could also add information about glitch Pokemon in White when you are typing an answer.

Assist Egg glitch
When Assist is used, it can use the moves of unhatched Eggs in the party.
By wtfhloser
Videos are currently unavailable on Bulbapedia; instead, you can watch the video on YouTube here.

Café Warehouse glitch
The tiles on the center and right of the door on the inside of the Café Warehouse say "It looks like a cabinet full of Pokémon goods." when the A Button is pressed while facing them.

Celestial tower glitch
When the B button is pressed on the 3rd and 4th floors of the Celestial Tower the NPC's will change directions, with the exception of the Nurse on the 3rd floor. This allows players to avoid all of the Trainers on these floors.

Dreamyard solid tiles bug
On the large staircase that can only be accessed post-game in the top-right of the Dreamyard, there is a row of solid tiles that cannot be walked on. On the others, these tiles can be walked on.
Fainted Pokémon glitch
Sometimes in a battle a Pokémon will survive a would-be one-hit KO with one HP left, but will still faint. This occurs more often to low level Pokémon.
In a Single Battle, this prevents the player from switching out Pokémon or attack. The only way out of this is to reset the game.
In a Rotation Battle, the Pokémon can still be rotated out to a different Pokémon.

Game layout peek
Often, when the game freezes when the player is walking about, standing, whatever, the freeze can produce some visual glitches, probably caused by the fact that such graphics are never saved on the console's temporary memory, such as:
Any nearby stairs look like ramps.
The umbrellas in Undella Town appear plain coloured.
The player and tall grass will disappear, and sometimes trees do too.

Gear Station glitch
When returning to Gear Station after riding a train from a location other than Gear Station, the location name "Gear Station" is not displayed until entering the center of the station, despite the platform itself being considered to be Gear Station by the game. This includes when the player reaches the rest area after seven wins in a row, since it is considered to be the Battle Subway by the game, but all other parts of the Battle Subway do not trigger this.

GTS freeze glitch
This glitch appears to happen when the game does not display the sprites of Trainers that have the sought Pokémon for trade. When selecting a Trainer after an empty space the game freezes. Tapping on a Trainer after a space will cause the game to display that an error has occurred.

Gym Leader music glitch
If the player is in the middle of a move that inflicts damage over several turns consecutively (such as Rollout) and the Gym Leader sends out their last Pokémon, the battle music will not change until after the duration of the move ends. This is because the Gym Leader does not come out to speak, which is what cues the music change.

Icirrus Gym glitch
In Icirrus Gym, there are three rocks which are not solid—they can be walked on. Using one of these rocks, it is possible to reach Brycen without battling Black Belt Thomas.

Landing on person or item
When Surfing, by moving towards a tile directly adjacent to an NPC or item that is adjacent to water, then pressing the D-pad to dismount onto the NPC or item, the player will be standing on top of it. However, this won't occur if the person is moving.

Liberty Garden Fly glitch
When selecting Liberty Garden while using Fly, its green dot is filled red as if it could be flown to, unlike other locations represented by the same symbol. This indicates that it may have been intended to be a location which could be flown to in the beta versions.
In the sequels however, all locations marked by green squares turn red.

Low HP cry glitch
While Pokémon with a yellow HP bar have a distorted cry to match their low HP, Pokémon with a red HP bar have the same cry as Pokémon with a green HP bar.

Music memory glitch
If the player goes below the first floor in the Dreamyard, Wellspring Cave, Chargestone Cave or Challenger's Cave, the music will usually play with a lower pitch and tempo. This is deliberate and is meant to set the atmosphere. However, if the player saves and resets, the music will play as if the player was on the top floor.
Likewise, if the player rides to a different area after getting on the bicycle, the music will change from the cycling theme to that location's music. However, if the player then saves and resets, the cycling music will play. (Interestingly, this did not occur in Generation IV.)
Variable scoring is not affected by this.

Music speed glitch
When the player uses Dig or an Escape Rope while cycling (cycling music must be playing) or surfing while below the first floor in Wellspring Cave, Chargestone Cave or Challenger's Cave and travels to Pinwheel Forest, Moor of Icirrus or Desert Resort, the music will play with a lower pitch and tempo, as if the player was in an underground floor. Reentering the affected area will revert the music back to normal, as will surfing or using the bicycle.

Mystery Gift Card Album cry glitch
If the player has a Wonder Card that contains a Pokémon on the next page to the one they are currently on, moves the cursor to "Exit" and taps the screen, the cry of the first card on that page will be heard.

Nacrene Gym bookcase glitch
After the bookcase in Nacrene Gym has been moved to reveal the secret stairs, it is still possible to read the book on the bookshelf from the stepladder. If the player stands on the stepladder, saves, then resets, upon resuming it is possible to read the book as if the bookcase had not moved. It is possible to do this until the player leaves the room.

Nimbasa Gym Trainer glitch
In Japanese versions of Pokémon Black and White, if the player loses to Lady Colette in Nimbasa Gym while directly facing her when encountered, this glitch will occur. When the player comes back in she will be standing on the same spot and will battle the player. After she is defeated, she still remains on the tracks of the roller coaster, and can be passed through while riding the roller coaster to Elesa.
By NaiJPC
Videos are currently unavailable on Bulbapedia; instead, you can watch the video on YouTube here.

Opelucid Gym air walk glitch
On the sloping part of the path before the first dragon's tail in Opelucid Gym, the two tiles directly up and down can be walked on, leaving the player walking on the air.

Opelucid Gym pedestal glitch
In front of both "certified Trainers" pedestals in the Opelucid Gym is an empty tile that cannot be walked on. This tile is interacted with rather than the pedestal itself, and acts just like it. The pedestal cannot be walked on, however.

Opelucid Gym shadowed tiles glitch
Yet another glitch in Opelucid Gym is that all of the tiles behind the Gym Leader can't be walked on.

Relic Castle glitch
On B3F of the Relic Castle near the drop point from the hole closest to the correct drop point to B2F there is a non-solid wall tile. It is on the wall one tile to the left of the wall directly to the south of this drop point.

Sitrus Berry glitch
If a Pokémon holding a Sitrus Berry hurts itself from confusion and reaches under half of its max HP through the damage, then its Sitrus Berry will not activate until another form of damage is dealt.

Shed Shell glitch
Sometimes in in-game battles, if the player's lead Pokémon holds a Shed Shell, it will be unable to switch out. This glitch does not occur in link battles.

Sky Drop glitch
This glitch can only occur in Double and Triple Battles. It is activated when Gravity is used while two Pokémon are in the semi-invulnerable state after Sky Drop is used. Gravity will bring the user of Sky Drop down while the target will be stuck in the semi-invulnerable state, unable to move until it is knocked out.

Text speed glitch
An old woman in Driftveil City talks one text speed slower than the selected text speed. This is due to her missing a large section of code, and is not intentional.

TM67 Retaliate glitch
In Japanese versions of Pokémon Black and White, TM67 (Retaliate) appears as a Dark-type TM, despite the move being Normal-type.

Trick Room glitch
If a Pokémon has an effective speed greater than 1809, it will ignore the effects of Trick Room and act before slower Pokémon.

Variable scoring glitch
This glitch only works in cities and towns that can be flown or teleported to with variable scoring dependent on the player's location in the area: Nacrene City (accordion player), Icirrus City (clapping group walking in a circle), and Opelucid City (harmonica player). If the player is in the area that the variable scoring is active, and flies or teleports to that same city or town, the variable scoring will be active until the music is changed, regardless of the player's location within the city or town. Likewise, if the player is in an area where the variable score is not active and flies or teleports to that city or town, the variable score will not activate until the music is changed.

Walking Trainer glitch
When blocking the path of certain Trainers who walk in a loop, if their path is blocked at a corner so that they cannot change direction, they will continue walking in the direction they were slowly and without turning, so as to appear to be walking into nothing but behaving as if they are walking into a wall.

Wellspring Cave glitch
When the B button is pressed on the 1st Basement floor of the Wellspring Cave the NPC's will start moving at different speeds depending on the Trainer. With some difficulty, this allows players to avoid all of the Trainers on the floor.